Welcome to GIS:SE @AntonioMaria! I think in simple terms: ESPG:32632 is a Projected coordinate system which uses metric units to calculate distances (usually metres); ESPG:4326 is a Geographic coordinate system which uses degree units and explains why you would be getting different results. When you save your file into another CRS, you are transforming the geometry of your features (your attributes remain the same).
– JosephJan 5 '18 at 12:33

1 Answer
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Results of $length are calculated using the units of the projection. Since 32632 is a UTM-projection, hence uses meter as unit, and 4326 uses degree, UTM-based calculations appear correct, or at least are more relatable.